Can anyone give me some hints on the following problem:
For integers x and y, show that if and only if and
Thanks in advance
Shinn
Hi
I don't see any very easy proof.
Maybe you can do that using a contraposition proof:
assume doesn't divide nor i.e. there are integers such that and
Then where
therefore i.e. does not divide
To prove compute all squares in
Another way to show that would be to say that is a factorial ring, that is an odd prime and so it is irreducible in and as a consequence